The grief generated by a divorce is about shattered dreams and concepts. It's very natural to process through the stages of grief, because your marriage has died. Once you've taken the appropriate amount of time for you to process the grief, it might now be time to consider dating again. Keep your children at the top of the considerations list as you prepare to enter into the dating game again.
To begin, assess how long your divorce has been final. Has it been a month, six months, a year? Everyone's time frame for when it is appropriate for you to start dating will vary. The only people that you need to consider when making this decision are your children. I'm not saying that you need to ask their permission; they might not be accepting of the idea for a while. I'm just saying that it is your job to assess the situation. How have they been acting? Do they ask you about finding some one new? How old are they? Are they little kids who really don't understand the situation fully, or are they older kids who really do know what is going on?
Second of all, you need to figure out your approach. If you do start dating, are you going to be open about it or keep it a secret from your children until you find some one that you want to be serious with? I have seen people take both of these paths. In my opinion, being open from the start is better. You may be opposed to this at first, but it really does ease them into the whole process. When a parent keeps it from them and all of a sudden is like "WHAM! This is my new boyfriend/girlfriend.It's too much of a challenge for some kids to have to handle.
Third, you're ready to begin to date again, so do it! How is that going to happen? Are people already trying to fix you up? You might already have a twinkle in your eye for someone? Would it be easier for you to sign up for an on-line dating website?
This should be an exciting time for you. You might not have been on a date in a long time, but it will all come rushing back. It's good to get past the grief of your divorce, begin dating again and meet new people even if nothing develops romantically. You can never have too many friends to share time and conversation with.